The invention relates generally to systems and methods for compensating for error in signals generated in a sigma delta circuit.
Sigma delta circuits are well known in the art of both digital and analog circuit designs. A Sigma delta circuit is a closed loop control system having a non-linear quantizing element in the loop. A sigma delta control loop may be referred to as a “modulator” implying its use as a means to create a modulated stream of output data that is quantized in time and amplitude from a possibly continuous input signal. The conventional sigma delta generally includes an input for receiving a signal, a differencing element and a filter having a transfer function that is configured to shape the noise generated by the amplitude and time quantizing element in the loop. Errors occur in such systems including tones and fixed pattern noise that are produced in the sigma delta loop. Remedies have been attempted to cure such errors, including complex dither schemes or MASH (“MASH” is the common term for a method employed to create a high order noise shaping loop with a cascade of low order noise shaping loops. A MASH design may therefore avoid the necessity of stabilizing a high order loop. The design of a MASH architecture may also allow spurious noise to be reduced because that noise is measured by a second or succeeding modulators in the cascade of modulator loops).
In a conventional sigma delta loop, a filter function H(s) is applied to an input signal prior to a quantizer, which can be represented as a source of noise, ε. Simple analysis of the loop shows: H(s)(x−y)+ε=y hence by rearrangement, assuming H is linear, and solving for y:
  y  =                              H          ⁡                      (            s            )                          ·        x                    1        +                  H          ⁡                      (            s            )                                +          ɛ              1        +                  H          ⁡                      (            s            )                              
from which we may extract the Signal Transfer function (STF)
  STF  =            H      ⁡              (        s        )                    1      +              H        ⁡                  (          s          )                    
and a Noise Transfer Function (NTF), to apply to ε the loop noise:
  NTF  =      1          1      +              H        ⁡                  (          s          )                    
The results are well known by those skilled in the art. At frequencies where H(s) is large Y is a close approximation to X and ε is suppressed by a large quantity. For example, if H(s) is chosen to be
            H      ⁡              (        s        )              =                  1        ⁢        e6            s        ,the noise is suppressed as frequency tends to zero and the signal has a limited bandwidth. The preceding analysis depends upon the assumption that the noise due to quantizing the signal may be represented as a uniform noise source ε, this is found to be only approximately valid in real examples. The assumption that ε is uniform within a certain bandwidth would suggest that the noise is monotonically decreasing with frequency if H(s) is monotonically increasing. In practice, artifacts exist in the noise of the system often referred to as tones or other spurious none-harmonically related signals present in the output data stream (Y). Various techniques exist to remove or reduce these artifacts. In one method, the complexity, and thus the order, of the loop is increased by making H(s) a second or higher order function, or ‘dither’ is added to the loop in an attempt to redistribute the spurious noise across the bandwidth, lessening the effect at a particular frequency. (The addition of dither describes a process where an out-of-band signal is superimposed on the input signal—the intention begin to disturb the artifact signals and possibly move them out of band as well). Neither of these techniques is precise. Even a higher order loop will show some artifacts and dither is not entirely effective at re-distributing the spurious noise.
Thus, there still exists a need for better methods of suppressing noise in a sigma delta loop. As will be observed, the invention accomplishes this in an elegant manner.